Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. II: QMR linear solver

Abstract

Linear systems in chemical physics often involve matrices with a certain sparse block structure. These can often be solved very effectively using iterative methods (sequence of matrix–vector products) in conjunction with a block Jacobi preconditioner [B. Poirier, Numer. Linear Algebra Appl. 7 (2000) 715]. In a two-part series, we present an efficient parallel implementation, incorporating several additional refinements. The present study (paper II) indicates that the basic parallel sparse matrix–vector product operation itself is the overall scalability bottleneck, faring much more poorly than the specialized, block Jacobi routines considered in a companion paper (paper I). However, a simple dimensional combination scheme is found to alleviate this difficulty.